Problem: $A$ $B$ $C$ If: $ AB = 6x + 6$, $ AC = 49$, and $ BC = 4x + 3$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {6x + 6} + {4x + 3} = {49}$ Combine like terms: $ 10x + 9 = {49}$ Subtract $9$ from both sides: $ 10x = 40$ Divide both sides by $10$ to find $x$ $ x = 4$ Substitute $4$ for $x$ in the expression that was given for $BC$ $ BC = 4({4}) + 3$ Simplify: $ {BC = 16 + 3}$ Simplify to find ${BC}$ : $ {BC = 19}$